There are many important petrophysical parameters used to interpret fluid flow in reservoirs and for calibrating appropriate reservoir simulation models. Among these are relative permeability, capillary pressure, saturation, spontaneous displacement, wettability, and resistivity, to name a few. In general, any one of those parameter can have different values during different modes of production such as the primary drainage mode, the imbibition mode, and the secondary drainage mode. The various parameter values for those different modes are conventionally determined (if at all) in the lab using two separate, time-consuming core flooding experiments. In addition to being time and labor intensive, a particular core sample can change during one of the experiments and adversely affect the results of the other.
In the prior art, there is no single experiment that allows one to determine all of those various parameter values. All those parameters are determined independently in the lab using special core analysis. Because the measurements are made during different experiments, using time-consuming methods, a full set of data on one single core plug can take a year or more to obtain. To run the different core flooding tests on the same sample, core cleanings are required, increasing the experimental time. It is generally preferred to run the complete experimental program on several core samples with similar properties, but it is difficult to ensure the different samples will behave similarly.
One method, known as the “semi-dynamic method”, allows one to obtain reliable estimates of many of those parameters. For example, the semi-dynamic method can be used to determine the capillary pressure for all three of the mentioned production modes, but determines the relative permeability for only certain modes. In addition, certain parameters, such as the relative permeability, is determined for each fluid present in the sample, typically brine and oil. Another method, referred to herein as “Li's relationship” or “Li's model” uses resistivity measurements to determine the relative permeability of conductive fluids such as brine. Other relationships, such as “Darcy's law for two immiscible phase flow”, the “Ramakrishan and Cappiello expression”, the “Brooks-Corey equation”, Pairoys' model for imbibition, and still others are known and used to determine certain parameter values. Each of those various relationships will be discussed further in the detailed description below. Obtaining all values for all stated parameters is referred to generally and herein as a “full petrophysical rock characterization”.